Here's how I did it just a few weeks ago. I was going from 3.2.2 source to 4.4.0 install but it'll work the same for 4.3.7

1. Backed up the database and the whole site directory.
2. Deleted all *.vb files in the 3.2.2 directory
3. Copied over 4.4.0 install over the original 3.2.2. files
4. Renamed the current web.config to something else (web.config.resources works well)
5. Opened both the renamed web.config and the release.config
6. Changed the connection string in the release.config to match the connection string from the old web.config (note: it has to be done twice and make sure you doing it in the right place. By default DNN 4.x is looking for a SQLExpress server and the SQL2000/2005 connection strings are commented out). Also copied over the MachineKey, ValidationKey, and DecryptionKey values to the release.config as per the DNN documentation.
7. Saved release.config as web.config
8. Set the site to run under .NET 2.0.xxxx in IIS
9. Launched the site and watched it go.

If I remember correctly there were a couple of SQL script errors on one of the sites but it's running fine so I didn't worry about them to much. I believe the errors were foreign key errors but the site started out under DNN 1 so I'm not overly surprised. On the other site I had no errors and it started out oringinally as a DNN 2 site.

If you post the errors you're running into it'll help solve the problems you're having. Without specifics we have to use a shotgun approach and try to cover everything instead of narrowing it down to a specific problem.